Yes, it normally means savory, it gives you an appetite. But no, when it comes down to the otaku world, everything would mean a different way. This term can be mostly found in 2ch in order to mean an extraordinary, crazy, or insane person or the likes. 香ばしい[koubashii] is an adjective, so you need to add a noun behind this, like 香ばしいやつ[koubashii yatsu or guy], 香ばしい書き込み[koubashii kakikomi or comment].
This origins from the TV CM of the famous snack, こうばしコーン[koubashi corn] which is one kind of とんがりコーン[tongari corn]. The CM used to be aired around 1997 or so, especially it could be seen midnight. A lot of anime fans who watched anime midnight came across this CM, and got influenced by such an extraordinary context. The quick song repeatedly said コーンだけでも香ばしいのに～ゴマだけでも香ばしいのに～♪[Just corn is savory, just sesame is savory]. This phrase lasted forever during the CM where a fox was cooking corn and a seal was cooking sesame (too bad, I couldn’t find the video). This weird CM hit otaku people, so that they started to use it to describe such a weirdie in 2ch.
There are some more similar words like KY, 痛い[itai, painful], 電波[dempa] or DQN[dokyun or dokyuso]. Sigh, such a weird is everywhere, but particularily in the otaku society, it could be notorious rapidly…The most 香ばしい comment I have ever seen was a long long dellusion he(?) had in mind…I like to have dellusion since I have some 2D thoughts, but I always have to be aware of the possibility that I could be such a 香ばしいやつ. つい最近もいたよそんなやつこのブログにも…あれは本当に香ばしかっt
Anyway, so long as we have a common sense, we are fine. If I am being a 香ばしいやつ, please stop me!